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'are convinced that' is correct and usable in written English.
You can use it to indicate that someone is very certain of something. For example: "We are convinced that this is the best course of action."
Dictionary
Exact(58)
There are analysts who are convinced that was the case.
Not all experts are convinced that will be enough, however.
"We are convinced that is who we are".
In these cases, we are convinced that PCR-positivity proves chronic Q fever.
They are convinced that they succeeded.
Democrats are convinced that he is right.
Some historians are convinced that millions died.
"People are convinced that he's politically persecuted," Mr. Grasso said.
But the newcomers are convinced that joining makes sense.
Sinhalese nationalists are convinced that the TNA has similar plans.
Other forecasters are convinced that a global recession is inevitable.
More suggestions(17)
are induced that
are confirmed that
are understood that
are believed that
are reassured that
are determined that
are explained that
are realized that
are demonstrated that
are concerned that
are persuaded that
are hopeful that
are secured that
are considered that
are guaranteed that
are convicted that
are involved that
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com